• 충청수학회지
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• 제37권1호
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• pp.27-40
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• 2024

In this paper, we consider the higher-order HartreeFock equations. The higher-order linear Schrödinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudorelativistic linear Schrödinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L² space but also proved that the solutions stay bounded uniformly in c. We address the remaining question on the convergence of higherorder Hartree-Fock equations when the Taylor expansion order is even. The distinguished feature from the odd case is that the group velocity of phase function would be vanishing when the size of frequency is comparable to c. Owing to this property, the kinetic energy of solutions is not coercive and only weaker Strichartz estimates compared to the odd case were obtained in [13]. Thus, we only manage to establish the existence of local solutions in H^s space for s > $\frac{1}{3}$ on a finite time interval [-T, T], however, the time interval does not depend on c and the solutions are bounded uniformly in c. In addition, we provide the convergence result of higher-order Hartree-Fock equations to the pseudo-relativistic equation with the same convergence rate as the odd case, which holds on [-T, T].

• Bulletin of the Korean Chemical Society
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• 제30권11호
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• pp.2617-2620
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• 2009

Using Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices the series expansion formulae in terms of multicenter overlap integrals of three complete orthonormal sets of ${\psi}^{\alpha}$‒exponential type orbitals and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule, where $\alpha$ = 1, 0, ‒1, ‒2,${\cdots}$. The formulae obtained can be useful for the study of interaction between atomic--molecular systems containing any number of closed and open shells when the ${\psi}^{\alpha}$‒exponential type basis functions and Coulomb-Yukawa like correlated interaction potentials are used in the Hartree-Fock-Roothaan and explicitly correlated approximations. The final results are valid for the arbitrary values of parameters of correlated interaction potentials and orbitals. As an example of application, the calculations have been performed for the potential energy of interaction between electron and molecule $H_2O$ using combined Hartree-Fock-Roothaan equations suggested by the author.

• 대한화학회지
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• 제29권1호
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• pp.3-8
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• 1985

Density functional theory에서의 전기음성도의 정의에 의해 전기음성도를 가전자(valence electron)만을 고려하여 구하였다. 전기음성도는 Hartree-Fock의 궤도 에너지(orbital energy)로 표시되는데 이로부터 구한 분자의 전기음성도 값은 다른 값들과 좋은 상관관계(correlation)를 보여준다. 또한 분자를 형성할 때 Sanderson의 법칙(electronegativity equalization principle)이 만족됨을 보였다.

• Journal of Electrical Engineering and Technology
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• 제9권5호
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• pp.1670-1676
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• 2014

This paper presents the modeling of Single Electron Transistor (SET) based on Physical model of a device and its equivalent circuit. The physical model is derived from Schrodinger equation. The wave function of the electrode is calculated using Hartree-Fock method and the quantum dot calculation is obtained from WKB approximation. The resulting wave functions are used to compute tunneling rates. From the tunneling rate the current is calculated. The equivalent circuit model discuss about the effect of capacitance on tunneling probability and free energy change. The parameters of equivalent circuit are extracted and optimized using genetic algorithm. The effect of tunneling probability, temperature variation effect on tunneling rate, coulomb blockade effect and current voltage characteristics are discussed.

• Bulletin of the Korean Chemical Society
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• 제15권11호
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• pp.953-957
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• 1994

Pseudospectral Hartree-Fock(PSHF) gradient calculations with $6-31G^{**}$ basis set have been carried out to determine the structure of D-Asparagine molecule $(C_4N_2O_3H_8)$ with improved grids and with the BFGS method. The modified PSHF method, despite partial optimization of the gradient code, turned out to be still faster than the conventional ab initio method, GAUSSIAN 90 program by more than twice. The optimum geometry of D-Asparagine obtained by the PSHF method is in good agreement with those calculated by the GAUSSIAN 90 program (within 0.0036 ${\AA}$ for bond lengths, 0.8 degrees for bond angles, and 1.6 degrees for torsional angles) except for three torsional angles. Here, rather large discrepancy of these three torsional angles (5-6 degrees) is attributed to the small differences in the optimum bond lengths and angles between the PSHF and GAUSSIAN 90 calculations.

• 대한화학회지
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• 제40권8호
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• pp.579-584
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• 1996

폴리엔의 HOMO-LUMO gap, 정적 및 동적인 3차 편극율을 시간의존 Hartree Fock 반경험적 PM3, AM1, MODO, MINDO/3 방법을 이용하여 구하였다. $C_2H_4$로부터 $C_{32}H_{34}$까지 모든 계산이 수행되었다. HOMO-LUMO gap은 MINDO/3>MNDO>PM3>AM1 순서로 증가하였으며, THG, DC-EFIDHG, IDRI, OKE효과는 AM1>MNDO>PM3 순서로 증가하였다. 다양한 3차 효과는 THG>DC-EFISHG>IDRI>OKE순서로 증가함을 보여주고 있다.

• 대한화학회지
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• 제40권5호
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• pp.317-326
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• 1996

Linear polyenes, ($C_4H_6\;to\;C_{30}H_{32}$)의 frequency dependent longitudinal polarizablilty, ${\alpha}zz(\omega)$ 와 second hyperpolarizabilities, ${\gamma}zzzz(\omega)$를 6-31G basis set에서 ab initio TDHF 이론을 사용하여 계산하였다. 폴리 아세틸렌의 frequency dispersion effect를 보기 위하여 외부 전기장의 주파수 영역에 광학성질을 구한후 무한 사슬을 갖는 고분자에 대하여 extrapolate하였다. 이때걸어준 외부 전기장에서의 광학적 성질에 대한 static field 에서의 광학성질의 비를 사용하여 비공면 영역에서의 dispersion effect를 고찰하였다. 또한 광학성질에 대한 주변 사슬의 효과를 조사하였으며 공명이 일어나는 영역에서의 광학 성질을 계산하기 위한 이론적 방법을 제안하였다.

• 대한화학회지
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• 제42권4호
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• pp.391-397
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• 1998

퓨란 고리를 포함하는 bis-furan lexitropsin에서, DNA minor groove의 염기쌍과 결합하는 중요 부분인 퓨란의 기하학적 구조를 반경험적 방법(MNDO)과 ab initio(Hartree-Fock) 방법으로 최적화 시켰다. 최적화된 구조에 대해 6-31G와 $6-31G^{\ast}$ basis set을 사용하여 전자적 구조와 양성자 친화도를 구하였다. 아울러 퓨란의 양성자 친화도에 미치는 치환기 효과를 알아보기 위해 전자를 주는 기와 전자를 끄는 기를 갖는 여러 치환 퓨란에 대해 양성자 친화도를 조사하였다. 그 결과 전자를 주는 기는 퓨란의 양성자 친화도를 증가시키는 반면 전자를 끄는 기는 양성자 친화도를 감소시켰으며, 이 결과 치환 퓨란의 산소 원자의 atomic charge와 전자밀도로 설명할 수 있었다

• Bulletin of the Korean Chemical Society
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• 제24권6호
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• pp.809-811
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• 2003

This brief review contains surveys of both four-component and two-component relativistic molecular theories. First the four-component relativistic approach is reviewed. Emphasis is placed on efficient computational schemes for the four-component Dirac-Hartree-Fock and Dirac-Kohn-Sham methods. Next, in the twocomponent relativistic framework, two relativistic Hamiltonians, RESC and higher-order Douglas-Kroll (DK), are introduced. An illustrative application is shown for the relativistic study on valence photoelectron spectrum of OsO₄. The developing four-component relativistic and approximate quasi-relativistic methods have been packed in a program suite named REL4D.

• EDISON SW 활용 경진대회 논문집
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• 제6회(2017년)
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• pp.11-15
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• 2017

We present a study of transition metal compounds using density functional theory (DFT), and density-corrected density functional theory(DC-DFT). By replacing the self-consistent density with that obtained from Hartree-Fock calculation, i.e., HF-DFT, the abnormality driven by self-interaction error is removed in several important cases. We discuss when and how HF-DFT works by examining 3d orbital dimers using approximate functionals and by comparing the results from self-consistent-DFT and HF-DFT with experimental values.